Question

A bank manager wishes to provide prompt service for customers at the bank’s drive- up window. The bank currently can serve up to 10 customers per 15- minute period without significant delay. The average arrival rate is 7 customers per 15- minute period. Let x denote the number of customers arriving per 15- minute period. Assuming x has a Poisson distribution:
a. Find the probability that 10 customers will arrive in a particular 15- minute period.
b. Find the probability that 10 or fewer customers will arrive in a particular 15- minute period.
c. Find the probability that there will be a significant delay at the drive- up window. That is, find the probability that more than 10 customers will arrive during a particular 15- minute period.